Blue Moon Blocking A Sunset

First note that radius of the blue circle is half the radius of the semicircle. Let $r$ be radius of blue circle and hence , the radius of semicircle is $2r$ . So ,

Area of blue circle $=\boxed{\pi r^2}$

Area of semicircle $=\dfrac{\pi(2r)^2}{2} = \dfrac{4\pi r^2}{2} =2\pi r^2$

Area of yellow region = (Area of semicircle) - (Area of blue circle) $=2\pi r^2-\pi r^2 = \boxed{\pi r^2}$

Clearly , Area of blue circle=Area of yellow region $= \boxed{\pi r^2}$ .